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Credit Swaps

Credit Swaps. Credit Default Swaps. Generic Credit Default Swap: Definition. In a standard credit default swap (CDS), a counterparty buys protection against default by a particular company or economic entity from a counterparty (seller).

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Credit Swaps

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  1. Credit Swaps Credit Default Swaps

  2. Generic Credit Default Swap: Definition • In a standard credit default swap (CDS), a counterparty buys protection against default by a particular company or economic entity from a counterparty (seller). • The company or entity is known as the reference entity and a default by that entity is known as a credit event. • The buyer of the CDS makes periodic payments or a premium to the seller until the end of the life of the CDS or until the credit event occurs.

  3. Generic Credit Default Swap: Definition • Depending on the contract, if the credit event occurs, the buyer has • The right to sell a particular bond (or loan) issued by the company for its par value (physical delivery) Or • Receive a cash settlement based on the difference between the defaulted bond’s par value and its market price (recovery value)

  4. Generic Credit Default Swap: Definition Example: • Suppose two parties enter into a 5-year CDS with a NP of $200,000,000. • The buyer agrees to pay 95 bp annually for protection against default by the reference entity. • If the reference entity does not default, the buyer does not receive a payoff and ends up paying $1,900,000 each year for 5 years. • If a credit event does occur, the buyer will receive the default payment and pay a final accrual payment on the unpaid premium.

  5. Generic Credit Default Swap: Definition Example: • Note: • If the event occurs half way through the year, then the buyer pays the seller $950,000. • If the swap contract calls for physical delivery, the buyer will sell $200 million par value of the defaulted bonds for $200,000,000. • If there is a cash settlement, then an agent will poll dealers to determine a mid-market value. If the recovery value were $30 per $100 face value, then the buyer would receive $140,000,000 minus the $950,000 accrued interest payment.

  6. CDS Terms • In the standard CDS, payments are usually made in arrears either on a quarter, semiannual, or annual basis. • The par value of the bond or debt is the notional principal used for determining the payments of the buyer. • In many CDS contracts, a number of bonds or credits can be delivered in the case of a default. • A company like Motorola, for example, might have 10 bonds with similar maturities, coupons, and embedded option and protection features that a buyer of a CDS could select in the event of a default.

  7. CDS Terms • In the event of a default, the payoff from the CDS is equal to the face value of the bond (or NP) minus the value of the bond just after the default. • The value of the bond just after the default expressed as a proportion of the bond’s face value is known as the recovery rate (RR). • If that value on the $200,000,000 CDS were $30 per $100 face value, then the recovery rate would be 30% and the payoff to the CDS buyer would be $140,000,000 minus any accrued payment. CDS Payoff = (1 − RR)NP – Accrued Payment Payoff = (1 −.30)$200,000,000) − Accrued Payment Payoff = $140,000,000 − Accrued Payment

  8. CDS Terms • The payments on a CDS are quoted as an annual percentage of the NP. • The payment is referred to as the CDS spread.

  9. CDS Terms • Swap bankers function as both brokers and dealers in the CDS market. • As dealers, they will provide bid and ask quotes on a particular credit entry. • For example, a swap bank might quote a 5-year CDS on a GE credit at 270 bp bid and 280 bp offer. • The swap bank will buy protection on GE for 2.7% of the underlying credit’s principal per year for 5 years • The swap bank will sell protection on GE for 2.8% of the principal.

  10. CDS Uses • CDS are used primarily to manage the credit risk on debt and fixed-income investment positions.

  11. CDS Uses Example 1: • Consider a bond fund manager who just purchased a 5-year BBB corporate bond at a price yielding 8% and wanted to eliminate the credit risk on the bond. • To eliminate default risk, suppose the manager bought a 5-year CDS on the bond. • If the spread on the CDS were equal to 2% of the bond’s principal, then the purchase of the CDS would have the effect of making the 8% BBB bond a risk-free bond yielding approximately 6%.

  12. CDS Uses Example 1: • That is, if the bond does not default, then the bond fund manager will receive 6% from owning the bond and the CDS (8% yield on bond – 2% payment on CDS). • If the bond defaults, then the bond manager would receive 6% from the bond and CDS up to the time of the default and then would receive the face value on the bond from the CDS seller, which the manager can reinvest for the remainder of the 5-year period. • Thus, the CDS allows the manager to reduce or eliminate the credit risk on the bond.

  13. CDS Uses Example 2: • Suppose a manager holding a portfolio of 5-year U.S. Treasury notes yielding 6% expected the economy to improve and therefore was willing to assume more credit risk in return for a higher return by buying BBB corporate bonds yielding 8%. • As an alternative to selling his Treasuries and buying the corporate bonds, the manager could sell a CDS.

  14. CDS Uses Example 2: • If he were to sell a 5-year CDS on the above 5-year BBB bond to a swap bank for the 2% spread, then the manager would be adding 2% to the 6% yield on his Treasuries to obtain an effective yield of 8%. • Thus with the CDS, the manager would be able to obtain an expected yield equivalent to the BBB bond yield and would also be assuming the same credit risk associated with that bond.

  15. CDS Uses Example 3: • Consider a commercial bank with a large loan to a corporation. • Prior to the introduction of CDS, the bank would typically have to hold on to the loan once it was created. • During this period, its only strategy for minimizing its loan portfolio’s exposure to credit risk was to create a diversified loan portfolio.

  16. CDS Uses Example 3: • With CDS, such a bank can now buy credit protection for the loan. • In general, CDSs allow banks and other financial institutions to more actively manage the credit risk on their loan portfolio, buying CDSs on some loans and selling CDSs on other. • Today, commercial banks are largest purchasers of CDS and insurance companies are the largest sellers.

  17. The Equilibrium CDS Spread

  18. The Equilibrium CDS Spread • In equilibrium, the payment or spread on a CDS should be approximately equal to the credit spread on the CDS’s underlying bond or credit.

  19. The Equilibrium CDS Spread Example: • If the only risk on a 5-year BBB corporate bond yielding 8% were credit risk and the risk-free rate on 5-year investment were 6%, then the bond would be trading in the market with a 2% credit spread.

  20. The Equilibrium CDS Spread Example: • If the spread on 5-year CDS on a BBB quality bond were 2%, then an investor could obtain a 5-year risk-free investment yielding 6% by either • Buying a 5-year Treasury or • Buying the 5-year BBB corporate yielding 8% and purchasing the CDS on the underlying credit at a 2% spread

  21. The Equilibrium CDS Spread Example: • If the spread on a CDS is not equal to the credit spread on the underlying bond, then an arbitrage opportunity would exist by taking positions in the bond, risk-free security, and the CDS.

  22. The Equilibrium CDS Spread CDS Spread = 1% < Credit Spread = 2% • Suppose a swap bank were offering the above CDS for 1% instead of 2%. • In this case, an investor looking for a 5-year risk-free investment would find it advantageous to create the synthetic risk-free investment with the BBB bond and the CDS. • That is, the investor could earn 1% more than the yield on the Treasury by creating a synthetic treasury by • Buying the 5-year BBB corporate yielding 8% and • Purchasing the CDS on the underlying credit at a 1%

  23. The Equilibrium CDS Spread CDS Spread = 1% < Credit Spread = 2% • If the swap bank were offering the above CDS for 1% instead of 2%, then an arbitrager could realized a free lunch equivalent to a 5-year cash flow of 1% of the par value of bond by • Shorting the Treasury at 6% (or borrowing at 6%) • Using the proceeds to buy the BBB corporate • Buying the CDS

  24. The Equilibrium CDS Spread CDS Spread = 1% < Credit Spread = 2% • These actions by investors and arbitrageurs, in turn, would have the impact of pushing the spread on the CDS towards 2%—the underlying bond’s credit spread.

  25. The Equilibrium CDS Spread CDS Spread = 3% > Credit Spread = 2% • If the swap bank were offering the CDS at a 3% spread, then an investor looking for a 5-year risk-free investment would obviously prefer a 6% Treasury yielding 6% to a synthetic risk-free investment formed with the 5-year BBB corporate yielding 8% and a CDS on the credit requiring a payment of 3%.

  26. The Equilibrium CDS Spread CDS Spread = 3% > Credit Spread = 2% • If the swap bank were offering the CDS at a 3% spread, then a more aggressive investor looking to invest in the higher yielding 5-year BBB bonds, though, could earn 1% more than the 8% on the BBB bond by creating a synthetic 5-year BBB bond by • Purchasing the 5-year Treasury at 6% • Selling the CDS at 3%

  27. The Equilibrium CDS Spread CDS Spread = 3% > Credit Spread = 2% • If the swap bank were offering the CDS at a 3% spread,thena bond portfolio manager holding 5-year BBB bonds yielding 8% could pick up an additional 1% yield with the same credit risk exposure by • Selling the BBB bonds • Selling the CDS at 3% • Using the proceeds from the bond sale to buy the 5-year Treasuries yielding 6%

  28. The Equilibrium CDS Spread CDS Spread = 3% > Credit Spread = 2% • If the swap bank were offering the CDS at a 3% spread, then an arbitrager could realized a free lunch equivalent to a 5-year cash flow of 1% of the par value on the bond by • Shorting the BBB bond • Selling the CDS • Using proceeds from bond sale to purchase 5-year Treasuries

  29. The Equilibrium CDS Spread CDS Spread = 3% > Credit Spread = 2% • With these positions, the arbitrageurwould receive for each of the next 5 years 6% from her Treasury investment and 3% from her CDS, but only pay 8% on her short BBB bond position. • Furthermore, her holdings of Treasury securities would enable her to cover her obligation on the CDS if there was a default. • That is, in the event of a default she would be able to pay the CDS holder from the net proceed from selling her Treasuries and closing her short BBB bond by buying back the corporate bonds at their defaulted recovery price.

  30. The Equilibrium CDS Spread CDS Spread = 3% > Credit Spread = 2% • Collectively, the actions of the investors, bond portfolio managers, and arbitrageur would have the effect of pushing the spread on CDS from 3% to 2%.

  31. The Equilibrium CDS Spread • In equilibrium, arbitrageurs and investors should ensure that the spreads on CDS are approximately equal to spreads on the underlying bond or credit. • This spread can be defined as the equilibrium spread and is referred to as the arbitrage-free spread and the Z-spread.

  32. CDS Spread and the Expected Default Loss • The arbitrage-free spread, Z, on a bond or CDS can also be thought of as the bond investor’s or CDS buyer’s expected loss from the principal from default.

  33. CDS Spread and the Expected Default Loss • Consider a portfolio of 5-year BBB bonds trading at a 2% credit spread. • The 2% premium that investors receive from the bond portfolio represents their compensation for an implied expected loss of 2% per year of the principal from the defaulted bonds.

  34. CDS Spread and the Expected Default Loss • If the spread were 2% and bond investors believed that the expected loss from default on such bonds would be only 1% per year of the principal, then the bond investors would want more BBB bonds, driving the price up and the yield down until the premium reflected a 1% spread. • If the spread were 2% and bond investors believed the default loss on a portfolio of BBB bond would be 3% per year, then the demand and price for such bonds would decrease, increasing the yield to reflect a credit spread of 3%.

  35. CDS Spread and the Expected Default Loss • Thus, inan efficient market, the credit spread on bonds and the equilibrium spreads on CDS represent the market’s implied expectation of the expected loss per year from the principal from default. • In the case of a CDS, the equilibrium spread can therefore be defined as the implied probability of default of principal on the contract.

  36. CDS Valuation

  37. CDS Valuation • The total value of a CDS’s payments is equal to the sum of the present values of the periodic CDS spread (Z) times the NP over the life of the CDS, discounted at the risk-free rate (R):

  38. CDS Valuation • In terms of the above example, the present value of the payment on the 5-year CDS with an equilibrium spread of 2% and a NP of $1 would be $0.084247:

  39. CDS Valuation • The buyer (seller) of this 5-year CDS would therefore be willing to make (receive) payments over five years that have a present value of $0.084247.

  40. CDS Valuation • Because the spread can also be viewed as an expected loss of principal, the present value of the payments is also equal to the expected default protection the buyer (seller) receives (pays). • The value of the CDS protection, in turn, is equal to the present value of the expected payout in the case of default.

  41. CDS Valuation • The present value of the expected payout in the case of default: • pt = probability of default in period t conditional on no earlier default. • RR = recovery rate (as a proportion of the face value) on the bond at the time of default. • NP = notional principal equal to the par value of the bond. where:

  42. CDS Valuation • Note that the probability of default, pt, is defined as a conditional probability of no prior defaults. • Thus the conditional probability of default in Year 4 is based on the probability that the bond will survive until Year 4. • In contrast, an unconditional probability is the likelihood that the bond will default at a given time as seen from the present.

  43. CDS Valuation • As noted in Chapter 5, conditional default probabilities are referred to as default intensities. • Over a period of time, these probabilities will change, increasing or decreasing depending on the quality of the credit.

  44. CDS Valuation • Instead of defining a CDS’s expected payout in terms periodic probability density, pt, the CDS’s expected payout can alternatively by defined by the average conditional default probability, :

  45. CDS Valuation • Given the equilibrium spread of .02 in our example and assuming a recovery rate of 30% if the underlying bond defaults, the implied probability density for our illustrative CDS would be .02857. • This implied probability is obtained by solving for the that makes the present value of the expected payout equal to present value of the payments of $.084247.

  46. CDS Valuation • The implied probability is obtained by solving for the that makes the present value of the expected payout equal to present value of the payments:

  47. CDS Valuation • Note that if there were no recovery (RR = 0), then the implied probability would be equal to the spread Z, which as noted can be thought of as the probability of default of principal. • The probability density implied by the market is referred to as the risk-neutral probability because it is based on an equilibrium spread that is arbitrage free.

  48. Alternative CDS Valuation

  49. Alternative CDS Valuation Approach • Suppose in the illustrative example, the estimated default intensity, sometimes referred to as the real world probability, on the 5-year BBB bond were .02 and not the implied probability of .02857.

  50. Alternative CDS Valuation Approach • In this case, the present value of the CDS expected payout would be $0.058973 instead of $0.084247:

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